A Jordan curve theorem with respect to a pretopology on Z(2)

作者：Slapal Josef^*

来源：International Journal of Computer Mathematics, 2013, 90(8): 1618-1628.

DOI：10.1080/00207160.2012.742889

• quasi-discrete pretopology
• quotient pretopology
• connectedness graph
• digital plane
• Jordan curve

We study a pretopology on Z(2) having the property that the Khalimsky topology is one of its quotient pretopologies. Using this fact, we prove an analogue of the Jordan curve theorem for this pretopology, thus showing that such a pretopology provides a large variety of digital Jordan curves. Some consequences of this result are discussed too.

• 出版日期2013-8-1